Noncommutative geometry and physics 2005 : proceedings of the International Sendai-Beijing Joint Workshop : Sendai, Japan, 1-4 November 2005, Beijing, China, 7-10 November 2005 / edited by Ursula Carow-Watamura [and others].

Includes bibliographical references.

This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems. Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.

I. Deformations and noncommutativity. 1. Expressions of algebra elements and transcendental noncommutative calculus / Hideki Omori [and others]. 2. Quasi-Hamiltonian quotients as disjoint unions of symplectic manifolds / Florent Schaffhauser. 3. Representations of Gauge transformation groups of higher Abelian gerbes / Kiyonori Gomi. 4. Algebroids associated with pre-poisson structures / Kentaro Mikami, Tadayoshi Mizutani. 5. Examples of groupoid / Naoya Miyazaki. 6. The cohomology of transitive lie algebroids / Z. Chen, Z.J. Liu. 7. Differential equations and Schwarzian derivatives / Hajime Sato, Tetsuya Ozawa, Hiroshi Suzuki. 8. Deformation of Batalin-Vilkovsky structure / Noriaki Ikeda -- II. Deformed Field theory and solutions. 9. Noncommutative solitons / Olaf Lechtenfeld. 10. Non-anti-commutative deformation of complex geometry / Sergei V. Ketov. 11. Seiberg-Witten monopole and young diagrams / Akifumi Sako. 12. Instanton counting, two dimensional Yang-Mills theory and topological strings / Kazutoshi Ohta. 13. Instantons in Non(anti)commutative Gauge theory via deformed ADHM construction / Takeo Araki, Tatsuhiko Takashima, Satoshi Watamur. 14. Noncommuative deformation and drinfel'd twisted symmetry / Yoshishige Kobayashi. 15. Affine lie superalgebra gl(2/2))(2k and twisted Conformal field theory / Xiang-Mao Ding, Gui-Dong Wang, Shi-Kun Wang. 16. A solution of Yang-Mills equation on BdS spacetime / Xin'an Ren, Shikun Wang. 17. Solitonic information transmission in general relativity / Yu Shang [and others]. 18. Difference discrete geometry on lattice / Ke Wu, Wei-Zhong Zhao, Han-Ying Guo.

English.

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